Question

Cono-Cool air conditioners cost $350 to purchase, result in electricity bills of $160 per year, and last for 5 years. Luxury Air models cost $550, result in electricity bills of $120 per year, and last for 8 years. The discount rate is 21%.

a. What are the equivalent annual costs of the Econo-Cool models? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b. What are the equivalent annual costs of the Luxury Air models? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

c. Which model is more cost-effective? Econo-Cool Luxury Air

d-1. Now you remember that the inflation rate is expected to be 10% per year for the foreseeable future. What are the equivalent annual costs of the Econo-Cool and Luxury Air models? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

d-2. Which model is more cost-effective? Econo-Cool Luxury Air

Answer 1

We calculate the equivalent annual costs of air conditioner models by determining the total costs including purchase and annual electricity bills, and converting these costs into an annual equivalent using the discount rate. Inflation also affects cost-effectiveness by increasing future costs, hence it is factored in. The model with the lower adjusted equivalent annual cost is the most cost-effective.

Step-by-step explanation:

To determine the equivalent annual costs of the Econo-Cool and Luxury Air models, we need to calculate the present value of the total costs across their respective lifespans and then convert this into an annual equivalent cost using the given discount rate.

For the Econo-Cool model:

• Purchase price: $350
• Annual electricity bill: $160 for 5 years
• Total cost over 5 years: $350 + ($160 x 5)
• Equivalent annual cost: (Total cost) / (Annuity factor at 21% for 5 years)

For the Luxury Air model:

• Purchase price: $550
• Annual electricity bill: $120 for 8 years
• Total cost over 8 years: $550 + ($120 x 8)
• Equivalent annual cost: (Total cost) / (Annuity factor at 21% for 8 years)

When adding an inflation rate of 10%, we have to adjust the calculation to factor in the higher electricity bills over time due to inflation. The modified equivalent annual costs must consider this increasing cost structure.

The cost-effective model can be determined by comparing the equivalent annual costs of both. After adjustments for inflation, the model with the lower equivalent annual cost is more cost-effective.

Answer 2

a) The equivalent annual costs of the Econo-Cool models= $436.50

b) The equivalent annual costs of the of Luxury Air models = $515

c)Econo-cool model

d 1 .(i) $464.15

(ii) $597.95

d 2 . Econo-cool model

Step-by-step explanation:

a) Econo-cool model

Purchase price= $350

Discount =21%

Electricity bill= $160 per year

Annual cost per year will be

$350 * 79/100 =$276.50 ------after applying the 21% discount

$276.50+$160 =$436.50 -------after adding electricity cost per year

The equivalent annual costs of the Econo-Cool models= $436.50

b) Luxury Air Models

Purchase price at the shop=$550

Discount =21%

Buying price =79/100*$500 = $395

Electricity cost = $120 per year

Annual cost = $395+$120 =$515

The equivalent annual costs of the of Luxury Air models = $515

c) The Econo-cool model

d (1) Econo-cool model

$350 *110/100 =$ 385 -----due to inflation

Apply the discount = 385*79/100 =$304.15

Add the cost of electricity = $304.15+$160 =$464.15

For Luxury Air model

$550*110/100 =$605

Apply the discount = $605*79/100 =$477.95

Add electricity bill = $477.95 +$120 =$597.95

d(2) Econo-cool model